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Titlebook: Deduction, Computation, Experiment; Exploring the Effect Rossella Lupacchini,Giovanna Corsi Book 2008 Springer-Verlag Milan 2008 Applied Ma

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发表于 2025-3-21 17:39:45 | 显示全部楼层 |阅读模式
书目名称Deduction, Computation, Experiment
副标题Exploring the Effect
编辑Rossella Lupacchini,Giovanna Corsi
视频video
图书封面Titlebook: Deduction, Computation, Experiment; Exploring the Effect Rossella Lupacchini,Giovanna Corsi Book 2008 Springer-Verlag Milan 2008 Applied Ma
描述This volume is located in a cross-disciplinary ?eld bringing together mat- matics, logic, natural science and philosophy. Re?ection on the e?ectiveness of proof brings out a number of questions that have always been latent in the informal understanding of the subject. What makes a symbolic constr- tion signi?cant? What makes an assumption reasonable? What makes a proof reliable? G¨ odel, Church and Turing, in di?erent ways, achieve a deep und- standing of the notion of e?ective calculability involved in the nature of proof. Turing’s work in particular provides a “precise and unquestionably adequate” de?nition of the general notion of a formal system in terms of a machine with a ?nite number of parts. On the other hand, Eugene Wigner refers to the - reasonable e?ectiveness of mathematics in the natural sciences as a miracle. Where should the boundary be traced between mathematical procedures and physical processes? What is the characteristic use of a proof as a com- tation, as opposed to its use as an experiment? What does natural science tell us about the e?ectiveness of proof? What is the role of mathematical proofs in the discovery and validation of empirical theories? The papers
出版日期Book 2008
关键词Applied Mathematics; Computation; Deduction; Experiment; logic; mathematics; proof
版次1
doihttps://doi.org/10.1007/978-88-470-0784-0
isbn_softcover978-88-470-0783-3
isbn_ebook978-88-470-0784-0
copyrightSpringer-Verlag Milan 2008
The information of publication is updating

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发表于 2025-3-22 00:10:55 | 显示全部楼层
,Automated Search for Gödel’s Proofs,isons with the literature are detailed in Section 4. (The general mathematical heuristics are indeed general: in Appendix . we show that they, together with two simple algebraic facts and the logical strategies, suffice to find a proof of “√2 is not rational”.)
发表于 2025-3-22 03:33:40 | 显示全部楼层
Book 2008res and physical processes? What is the characteristic use of a proof as a com- tation, as opposed to its use as an experiment? What does natural science tell us about the e?ectiveness of proof? What is the role of mathematical proofs in the discovery and validation of empirical theories? The papers
发表于 2025-3-22 05:34:47 | 显示全部楼层
发表于 2025-3-22 10:30:35 | 显示全部楼层
The Logic of the Weak Excluded Middle: A Case Study of Proof-Search,ountermodel? It is a well known result [.] that Lemma 1. (Hosoi) If a wff A contains the propositional letters ..,...,.. then A is a theorem of J iff (¬.. ⋁ ¬¬..) ⋀ ⋯ ⋀ (¬.. ⋁ ¬¬..) → . is a theorem of the intuitionistic logic.
发表于 2025-3-22 14:04:33 | 显示全部楼层
Quantum Combing,anguage theory, finite group theory, and quantum computation theory can lead to new views. As working study-case the problem of combing finite groups will be dealt with, which bridges language theoretical issues with structural and algorithmic issues.
发表于 2025-3-22 19:23:05 | 显示全部楼层
?ectiveness of proof brings out a number of questions that have always been latent in the informal understanding of the subject. What makes a symbolic constr- tion signi?cant? What makes an assumption reasonable? What makes a proof reliable? G¨ odel, Church and Turing, in di?erent ways, achieve a de
发表于 2025-3-22 22:37:40 | 显示全部楼层
https://doi.org/10.1007/978-3-642-91522-2 than experiments. ‘Theoretical Mathematics’, a new synthesis of mathematics and theoretical physics proposed by Jaffe and Quinn in the 1990’s [12], looks at pure mathematics as a sort of experimental testing ground for certain physical theories (and in particular for associated toy models).
发表于 2025-3-23 05:18:39 | 显示全部楼层
Schmerzmessung und -dokumentatione the bilateral symmetry coupling any possibility with its negation, sized by “complex probability amplitudes”, may dissolve the ‘ignorance’ of classical probabilities as well as the ‘blindness’ of finite mechanical procedures.
发表于 2025-3-23 09:17:51 | 显示全部楼层
Toy Models in Physics and the Reasonable Effectiveness of Mathematics, than experiments. ‘Theoretical Mathematics’, a new synthesis of mathematics and theoretical physics proposed by Jaffe and Quinn in the 1990’s [12], looks at pure mathematics as a sort of experimental testing ground for certain physical theories (and in particular for associated toy models).
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